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Elementary Mechanics of Solids by P. P. Benham and B. G. Neal (Auth.)

By P. P. Benham and B. G. Neal (Auth.)

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Determine also the lateral stress as a function of the axial stress. 11. A thin-walled steel cylinder of internal radius 5 in. and wall thickness i in. is cooled through 50°C. Determine values for the internal pressure and axial load which, if applied, would restore the cylinder to its original dimen­ sions. a = 11 x 10" 6 /°C; E = 30 x 106 lb/in2; v = 0-3. 1. Introduction In the problems discussed in the previous chapters the stress planes analysed had only one component of stress acting on them.

23) where a and b are as shown in Fig. 8. Load Deformation For vertical central load T Ί - = k; F = K. 24) y y For rotation due to the offset load AT _ δ ~k; AF δ' K. 27) 46 E L E M E N T A R Y M E C H A N I C S OF S O L I D S Solution There are thus eight equations above to solve for the eight unknown quantities. 28) _ »* A + kya + 2 _ 0. 8. General Stress-Strain Relationships A bar which is extended under tensile stress will also undergo a contraction in the transverse direction. The strain which occurs perpendicular to the direction of a stress is termed lateral or transverse strain and is found to be of opposite sign and pro­ portional, in the elastic range, to the strain in the direction of the stress.

E. the force per unit area. Likewise the deformation of different bodies sub­ jected to a particular load is a function of size and therefore comparisons are made by expressing deformation as a nondimensional quantity given by the change in dimension per unit of original dimension, or in the case of shear as a change in angle between two initially perpendicular planes. The nondimensional expression of deformation is termed strain. Direct or Normal Strain Consider the bar shown in Fig. 2 subjected to axial tensile loading if the resulting extension of the bar is δΐ and its original length is /0, then the direct tensile strain is δί -τ0 28 ELEMENTARY MECHANICS OF SOLIDS If two bars identical in material, length /0, and area were each subjected to a tensile force P then the extension in each would be the same, say δΐ, and the strain <5///0.

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